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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.03642 |
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| _version_ | 1866908375559700480 |
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| author | Merlet, Benoît Venel, Juliette Zurek, Antoine |
| author_facet | Merlet, Benoît Venel, Juliette Zurek, Antoine |
| contents | This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is introduced and studied. The model describes some mechanisms involved in corrosion processes at the surface of carbon steel canisters in contact with a claystone formation. The main objective of the paper is to prove the existence of weak solutions to the problem which are maximal in time. For this, a time semidiscrete minimizing movements scheme based on a Wasserstein-like distance is introduced. The existence of solutions to the scheme is proved. Then, using a priori estimates, it is shown that as the time step goes to zero these solutions converge up to extraction towards a maximal weak solution to the free boundary model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_03642 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Analysis of a one dimensional energy dissipating free boundary model with nonlinear boundary conditions. Existence of weak solutions Merlet, Benoît Venel, Juliette Zurek, Antoine Analysis of PDEs This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is introduced and studied. The model describes some mechanisms involved in corrosion processes at the surface of carbon steel canisters in contact with a claystone formation. The main objective of the paper is to prove the existence of weak solutions to the problem which are maximal in time. For this, a time semidiscrete minimizing movements scheme based on a Wasserstein-like distance is introduced. The existence of solutions to the scheme is proved. Then, using a priori estimates, it is shown that as the time step goes to zero these solutions converge up to extraction towards a maximal weak solution to the free boundary model. |
| title | Analysis of a one dimensional energy dissipating free boundary model with nonlinear boundary conditions. Existence of weak solutions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2212.03642 |